Properties

Label 825.2.k.c.518.1
Level $825$
Weight $2$
Character 825.518
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 518.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 825.518
Dual form 825.2.k.c.782.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70711 - 1.70711i) q^{2} +(1.41421 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 - 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.70711 - 1.70711i) q^{2} +(1.41421 + 1.00000i) q^{3} +3.82843i q^{4} +(-0.707107 - 4.12132i) q^{6} +(0.585786 - 0.585786i) q^{7} +(3.12132 - 3.12132i) q^{8} +(1.00000 + 2.82843i) q^{9} -1.00000i q^{11} +(-3.82843 + 5.41421i) q^{12} +(2.00000 + 2.00000i) q^{13} -2.00000 q^{14} -3.00000 q^{16} +(2.82843 + 2.82843i) q^{17} +(3.12132 - 6.53553i) q^{18} -2.82843i q^{19} +(1.41421 - 0.242641i) q^{21} +(-1.70711 + 1.70711i) q^{22} +(-5.24264 + 5.24264i) q^{23} +(7.53553 - 1.29289i) q^{24} -6.82843i q^{26} +(-1.41421 + 5.00000i) q^{27} +(2.24264 + 2.24264i) q^{28} +4.82843 q^{29} -8.82843 q^{31} +(-1.12132 - 1.12132i) q^{32} +(1.00000 - 1.41421i) q^{33} -9.65685i q^{34} +(-10.8284 + 3.82843i) q^{36} +(5.82843 - 5.82843i) q^{37} +(-4.82843 + 4.82843i) q^{38} +(0.828427 + 4.82843i) q^{39} +3.65685i q^{41} +(-2.82843 - 2.00000i) q^{42} +(8.24264 + 8.24264i) q^{43} +3.82843 q^{44} +17.8995 q^{46} +(1.24264 + 1.24264i) q^{47} +(-4.24264 - 3.00000i) q^{48} +6.31371i q^{49} +(1.17157 + 6.82843i) q^{51} +(-7.65685 + 7.65685i) q^{52} +(1.00000 - 1.00000i) q^{53} +(10.9497 - 6.12132i) q^{54} -3.65685i q^{56} +(2.82843 - 4.00000i) q^{57} +(-8.24264 - 8.24264i) q^{58} +4.00000 q^{59} +10.4853 q^{61} +(15.0711 + 15.0711i) q^{62} +(2.24264 + 1.07107i) q^{63} +9.82843i q^{64} +(-4.12132 + 0.707107i) q^{66} +(3.58579 - 3.58579i) q^{67} +(-10.8284 + 10.8284i) q^{68} +(-12.6569 + 2.17157i) q^{69} +14.4853i q^{71} +(11.9497 + 5.70711i) q^{72} -19.8995 q^{74} +10.8284 q^{76} +(-0.585786 - 0.585786i) q^{77} +(6.82843 - 9.65685i) q^{78} -5.17157i q^{79} +(-7.00000 + 5.65685i) q^{81} +(6.24264 - 6.24264i) q^{82} +(5.07107 - 5.07107i) q^{83} +(0.928932 + 5.41421i) q^{84} -28.1421i q^{86} +(6.82843 + 4.82843i) q^{87} +(-3.12132 - 3.12132i) q^{88} -1.65685 q^{89} +2.34315 q^{91} +(-20.0711 - 20.0711i) q^{92} +(-12.4853 - 8.82843i) q^{93} -4.24264i q^{94} +(-0.464466 - 2.70711i) q^{96} +(0.656854 - 0.656854i) q^{97} +(10.7782 - 10.7782i) q^{98} +(2.82843 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} + 8q^{7} + 4q^{8} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{2} + 8q^{7} + 4q^{8} + 4q^{9} - 4q^{12} + 8q^{13} - 8q^{14} - 12q^{16} + 4q^{18} - 4q^{22} - 4q^{23} + 16q^{24} - 8q^{28} + 8q^{29} - 24q^{31} + 4q^{32} + 4q^{33} - 32q^{36} + 12q^{37} - 8q^{38} - 8q^{39} + 16q^{43} + 4q^{44} + 32q^{46} - 12q^{47} + 16q^{51} - 8q^{52} + 4q^{53} + 24q^{54} - 16q^{58} + 16q^{59} + 8q^{61} + 32q^{62} - 8q^{63} - 8q^{66} + 20q^{67} - 32q^{68} - 28q^{69} + 28q^{72} - 40q^{74} + 32q^{76} - 8q^{77} + 16q^{78} - 28q^{81} + 8q^{82} - 8q^{83} + 32q^{84} + 16q^{87} - 4q^{88} + 16q^{89} + 32q^{91} - 52q^{92} - 16q^{93} - 16q^{96} - 20q^{97} + 12q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70711 1.70711i −1.20711 1.20711i −0.971960 0.235147i \(-0.924443\pi\)
−0.235147 0.971960i \(-0.575557\pi\)
\(3\) 1.41421 + 1.00000i 0.816497 + 0.577350i
\(4\) 3.82843i 1.91421i
\(5\) 0 0
\(6\) −0.707107 4.12132i −0.288675 1.68252i
\(7\) 0.585786 0.585786i 0.221406 0.221406i −0.587684 0.809091i \(-0.699960\pi\)
0.809091 + 0.587684i \(0.199960\pi\)
\(8\) 3.12132 3.12132i 1.10355 1.10355i
\(9\) 1.00000 + 2.82843i 0.333333 + 0.942809i
\(10\) 0 0
\(11\) 1.00000i 0.301511i
\(12\) −3.82843 + 5.41421i −1.10517 + 1.56295i
\(13\) 2.00000 + 2.00000i 0.554700 + 0.554700i 0.927794 0.373094i \(-0.121703\pi\)
−0.373094 + 0.927794i \(0.621703\pi\)
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −3.00000 −0.750000
\(17\) 2.82843 + 2.82843i 0.685994 + 0.685994i 0.961344 0.275350i \(-0.0887937\pi\)
−0.275350 + 0.961344i \(0.588794\pi\)
\(18\) 3.12132 6.53553i 0.735702 1.54044i
\(19\) 2.82843i 0.648886i −0.945905 0.324443i \(-0.894823\pi\)
0.945905 0.324443i \(-0.105177\pi\)
\(20\) 0 0
\(21\) 1.41421 0.242641i 0.308607 0.0529485i
\(22\) −1.70711 + 1.70711i −0.363956 + 0.363956i
\(23\) −5.24264 + 5.24264i −1.09317 + 1.09317i −0.0979775 + 0.995189i \(0.531237\pi\)
−0.995189 + 0.0979775i \(0.968763\pi\)
\(24\) 7.53553 1.29289i 1.53818 0.263911i
\(25\) 0 0
\(26\) 6.82843i 1.33916i
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) 2.24264 + 2.24264i 0.423819 + 0.423819i
\(29\) 4.82843 0.896616 0.448308 0.893879i \(-0.352027\pi\)
0.448308 + 0.893879i \(0.352027\pi\)
\(30\) 0 0
\(31\) −8.82843 −1.58563 −0.792816 0.609461i \(-0.791386\pi\)
−0.792816 + 0.609461i \(0.791386\pi\)
\(32\) −1.12132 1.12132i −0.198223 0.198223i
\(33\) 1.00000 1.41421i 0.174078 0.246183i
\(34\) 9.65685i 1.65614i
\(35\) 0 0
\(36\) −10.8284 + 3.82843i −1.80474 + 0.638071i
\(37\) 5.82843 5.82843i 0.958188 0.958188i −0.0409727 0.999160i \(-0.513046\pi\)
0.999160 + 0.0409727i \(0.0130457\pi\)
\(38\) −4.82843 + 4.82843i −0.783274 + 0.783274i
\(39\) 0.828427 + 4.82843i 0.132655 + 0.773167i
\(40\) 0 0
\(41\) 3.65685i 0.571105i 0.958363 + 0.285552i \(0.0921770\pi\)
−0.958363 + 0.285552i \(0.907823\pi\)
\(42\) −2.82843 2.00000i −0.436436 0.308607i
\(43\) 8.24264 + 8.24264i 1.25699 + 1.25699i 0.952522 + 0.304469i \(0.0984788\pi\)
0.304469 + 0.952522i \(0.401521\pi\)
\(44\) 3.82843 0.577157
\(45\) 0 0
\(46\) 17.8995 2.63914
\(47\) 1.24264 + 1.24264i 0.181258 + 0.181258i 0.791904 0.610646i \(-0.209090\pi\)
−0.610646 + 0.791904i \(0.709090\pi\)
\(48\) −4.24264 3.00000i −0.612372 0.433013i
\(49\) 6.31371i 0.901958i
\(50\) 0 0
\(51\) 1.17157 + 6.82843i 0.164053 + 0.956171i
\(52\) −7.65685 + 7.65685i −1.06181 + 1.06181i
\(53\) 1.00000 1.00000i 0.137361 0.137361i −0.635083 0.772444i \(-0.719034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(54\) 10.9497 6.12132i 1.49007 0.833006i
\(55\) 0 0
\(56\) 3.65685i 0.488668i
\(57\) 2.82843 4.00000i 0.374634 0.529813i
\(58\) −8.24264 8.24264i −1.08231 1.08231i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 10.4853 1.34250 0.671251 0.741230i \(-0.265757\pi\)
0.671251 + 0.741230i \(0.265757\pi\)
\(62\) 15.0711 + 15.0711i 1.91403 + 1.91403i
\(63\) 2.24264 + 1.07107i 0.282546 + 0.134942i
\(64\) 9.82843i 1.22855i
\(65\) 0 0
\(66\) −4.12132 + 0.707107i −0.507299 + 0.0870388i
\(67\) 3.58579 3.58579i 0.438074 0.438074i −0.453290 0.891363i \(-0.649750\pi\)
0.891363 + 0.453290i \(0.149750\pi\)
\(68\) −10.8284 + 10.8284i −1.31314 + 1.31314i
\(69\) −12.6569 + 2.17157i −1.52371 + 0.261427i
\(70\) 0 0
\(71\) 14.4853i 1.71909i 0.511063 + 0.859543i \(0.329252\pi\)
−0.511063 + 0.859543i \(0.670748\pi\)
\(72\) 11.9497 + 5.70711i 1.40829 + 0.672589i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) −19.8995 −2.31327
\(75\) 0 0
\(76\) 10.8284 1.24211
\(77\) −0.585786 0.585786i −0.0667566 0.0667566i
\(78\) 6.82843 9.65685i 0.773167 1.09342i
\(79\) 5.17157i 0.581847i −0.956746 0.290924i \(-0.906037\pi\)
0.956746 0.290924i \(-0.0939626\pi\)
\(80\) 0 0
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 6.24264 6.24264i 0.689384 0.689384i
\(83\) 5.07107 5.07107i 0.556622 0.556622i −0.371722 0.928344i \(-0.621233\pi\)
0.928344 + 0.371722i \(0.121233\pi\)
\(84\) 0.928932 + 5.41421i 0.101355 + 0.590739i
\(85\) 0 0
\(86\) 28.1421i 3.03464i
\(87\) 6.82843 + 4.82843i 0.732084 + 0.517662i
\(88\) −3.12132 3.12132i −0.332734 0.332734i
\(89\) −1.65685 −0.175626 −0.0878131 0.996137i \(-0.527988\pi\)
−0.0878131 + 0.996137i \(0.527988\pi\)
\(90\) 0 0
\(91\) 2.34315 0.245628
\(92\) −20.0711 20.0711i −2.09255 2.09255i
\(93\) −12.4853 8.82843i −1.29466 0.915465i
\(94\) 4.24264i 0.437595i
\(95\) 0 0
\(96\) −0.464466 2.70711i −0.0474044 0.276293i
\(97\) 0.656854 0.656854i 0.0666934 0.0666934i −0.672973 0.739667i \(-0.734983\pi\)
0.739667 + 0.672973i \(0.234983\pi\)
\(98\) 10.7782 10.7782i 1.08876 1.08876i
\(99\) 2.82843 1.00000i 0.284268 0.100504i
\(100\) 0 0
\(101\) 12.8284i 1.27648i −0.769839 0.638238i \(-0.779664\pi\)
0.769839 0.638238i \(-0.220336\pi\)
\(102\) 9.65685 13.6569i 0.956171 1.35223i
\(103\) 3.58579 + 3.58579i 0.353318 + 0.353318i 0.861343 0.508025i \(-0.169624\pi\)
−0.508025 + 0.861343i \(0.669624\pi\)
\(104\) 12.4853 1.22428
\(105\) 0 0
\(106\) −3.41421 −0.331618
\(107\) −8.24264 8.24264i −0.796846 0.796846i 0.185751 0.982597i \(-0.440528\pi\)
−0.982597 + 0.185751i \(0.940528\pi\)
\(108\) −19.1421 5.41421i −1.84195 0.520983i
\(109\) 8.82843i 0.845610i −0.906221 0.422805i \(-0.861046\pi\)
0.906221 0.422805i \(-0.138954\pi\)
\(110\) 0 0
\(111\) 14.0711 2.41421i 1.33557 0.229147i
\(112\) −1.75736 + 1.75736i −0.166055 + 0.166055i
\(113\) −0.171573 + 0.171573i −0.0161402 + 0.0161402i −0.715131 0.698991i \(-0.753633\pi\)
0.698991 + 0.715131i \(0.253633\pi\)
\(114\) −11.6569 + 2.00000i −1.09176 + 0.187317i
\(115\) 0 0
\(116\) 18.4853i 1.71632i
\(117\) −3.65685 + 7.65685i −0.338076 + 0.707876i
\(118\) −6.82843 6.82843i −0.628608 0.628608i
\(119\) 3.31371 0.303767
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −17.8995 17.8995i −1.62054 1.62054i
\(123\) −3.65685 + 5.17157i −0.329727 + 0.466305i
\(124\) 33.7990i 3.03524i
\(125\) 0 0
\(126\) −2.00000 5.65685i −0.178174 0.503953i
\(127\) 1.41421 1.41421i 0.125491 0.125491i −0.641572 0.767063i \(-0.721717\pi\)
0.767063 + 0.641572i \(0.221717\pi\)
\(128\) 14.5355 14.5355i 1.28477 1.28477i
\(129\) 3.41421 + 19.8995i 0.300605 + 1.75205i
\(130\) 0 0
\(131\) 1.17157i 0.102361i 0.998689 + 0.0511804i \(0.0162983\pi\)
−0.998689 + 0.0511804i \(0.983702\pi\)
\(132\) 5.41421 + 3.82843i 0.471247 + 0.333222i
\(133\) −1.65685 1.65685i −0.143667 0.143667i
\(134\) −12.2426 −1.05760
\(135\) 0 0
\(136\) 17.6569 1.51406
\(137\) 5.82843 + 5.82843i 0.497956 + 0.497956i 0.910801 0.412845i \(-0.135465\pi\)
−0.412845 + 0.910801i \(0.635465\pi\)
\(138\) 25.3137 + 17.8995i 2.15485 + 1.52371i
\(139\) 6.34315i 0.538019i 0.963138 + 0.269009i \(0.0866962\pi\)
−0.963138 + 0.269009i \(0.913304\pi\)
\(140\) 0 0
\(141\) 0.514719 + 3.00000i 0.0433471 + 0.252646i
\(142\) 24.7279 24.7279i 2.07512 2.07512i
\(143\) 2.00000 2.00000i 0.167248 0.167248i
\(144\) −3.00000 8.48528i −0.250000 0.707107i
\(145\) 0 0
\(146\) 0 0
\(147\) −6.31371 + 8.92893i −0.520746 + 0.736446i
\(148\) 22.3137 + 22.3137i 1.83418 + 1.83418i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) −18.1421 −1.47639 −0.738193 0.674590i \(-0.764321\pi\)
−0.738193 + 0.674590i \(0.764321\pi\)
\(152\) −8.82843 8.82843i −0.716080 0.716080i
\(153\) −5.17157 + 10.8284i −0.418097 + 0.875426i
\(154\) 2.00000i 0.161165i
\(155\) 0 0
\(156\) −18.4853 + 3.17157i −1.48001 + 0.253929i
\(157\) −7.48528 + 7.48528i −0.597390 + 0.597390i −0.939617 0.342227i \(-0.888819\pi\)
0.342227 + 0.939617i \(0.388819\pi\)
\(158\) −8.82843 + 8.82843i −0.702352 + 0.702352i
\(159\) 2.41421 0.414214i 0.191460 0.0328493i
\(160\) 0 0
\(161\) 6.14214i 0.484068i
\(162\) 21.6066 + 2.29289i 1.69757 + 0.180147i
\(163\) −6.41421 6.41421i −0.502400 0.502400i 0.409783 0.912183i \(-0.365604\pi\)
−0.912183 + 0.409783i \(0.865604\pi\)
\(164\) −14.0000 −1.09322
\(165\) 0 0
\(166\) −17.3137 −1.34380
\(167\) −10.7279 10.7279i −0.830152 0.830152i 0.157386 0.987537i \(-0.449693\pi\)
−0.987537 + 0.157386i \(0.949693\pi\)
\(168\) 3.65685 5.17157i 0.282132 0.398996i
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 8.00000 2.82843i 0.611775 0.216295i
\(172\) −31.5563 + 31.5563i −2.40615 + 2.40615i
\(173\) −8.48528 + 8.48528i −0.645124 + 0.645124i −0.951811 0.306687i \(-0.900780\pi\)
0.306687 + 0.951811i \(0.400780\pi\)
\(174\) −3.41421 19.8995i −0.258831 1.50858i
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) 5.65685 + 4.00000i 0.425195 + 0.300658i
\(178\) 2.82843 + 2.82843i 0.212000 + 0.212000i
\(179\) 4.14214 0.309598 0.154799 0.987946i \(-0.450527\pi\)
0.154799 + 0.987946i \(0.450527\pi\)
\(180\) 0 0
\(181\) −5.65685 −0.420471 −0.210235 0.977651i \(-0.567423\pi\)
−0.210235 + 0.977651i \(0.567423\pi\)
\(182\) −4.00000 4.00000i −0.296500 0.296500i
\(183\) 14.8284 + 10.4853i 1.09615 + 0.775094i
\(184\) 32.7279i 2.41273i
\(185\) 0 0
\(186\) 6.24264 + 36.3848i 0.457733 + 2.66786i
\(187\) 2.82843 2.82843i 0.206835 0.206835i
\(188\) −4.75736 + 4.75736i −0.346966 + 0.346966i
\(189\) 2.10051 + 3.75736i 0.152789 + 0.273308i
\(190\) 0 0
\(191\) 11.3137i 0.818631i −0.912393 0.409316i \(-0.865768\pi\)
0.912393 0.409316i \(-0.134232\pi\)
\(192\) −9.82843 + 13.8995i −0.709306 + 1.00311i
\(193\) −8.00000 8.00000i −0.575853 0.575853i 0.357905 0.933758i \(-0.383491\pi\)
−0.933758 + 0.357905i \(0.883491\pi\)
\(194\) −2.24264 −0.161012
\(195\) 0 0
\(196\) −24.1716 −1.72654
\(197\) 14.1421 + 14.1421i 1.00759 + 1.00759i 0.999971 + 0.00761443i \(0.00242377\pi\)
0.00761443 + 0.999971i \(0.497576\pi\)
\(198\) −6.53553 3.12132i −0.464460 0.221823i
\(199\) 2.48528i 0.176177i −0.996113 0.0880885i \(-0.971924\pi\)
0.996113 0.0880885i \(-0.0280758\pi\)
\(200\) 0 0
\(201\) 8.65685 1.48528i 0.610607 0.104764i
\(202\) −21.8995 + 21.8995i −1.54084 + 1.54084i
\(203\) 2.82843 2.82843i 0.198517 0.198517i
\(204\) −26.1421 + 4.48528i −1.83032 + 0.314033i
\(205\) 0 0
\(206\) 12.2426i 0.852985i
\(207\) −20.0711 9.58579i −1.39504 0.666258i
\(208\) −6.00000 6.00000i −0.416025 0.416025i
\(209\) −2.82843 −0.195646
\(210\) 0 0
\(211\) 12.4853 0.859522 0.429761 0.902943i \(-0.358598\pi\)
0.429761 + 0.902943i \(0.358598\pi\)
\(212\) 3.82843 + 3.82843i 0.262937 + 0.262937i
\(213\) −14.4853 + 20.4853i −0.992515 + 1.40363i
\(214\) 28.1421i 1.92376i
\(215\) 0 0
\(216\) 11.1924 + 20.0208i 0.761546 + 1.36224i
\(217\) −5.17157 + 5.17157i −0.351069 + 0.351069i
\(218\) −15.0711 + 15.0711i −1.02074 + 1.02074i
\(219\) 0 0
\(220\) 0 0
\(221\) 11.3137i 0.761042i
\(222\) −28.1421 19.8995i −1.88878 1.33557i
\(223\) −14.5563 14.5563i −0.974765 0.974765i 0.0249241 0.999689i \(-0.492066\pi\)
−0.999689 + 0.0249241i \(0.992066\pi\)
\(224\) −1.31371 −0.0877758
\(225\) 0 0
\(226\) 0.585786 0.0389659
\(227\) 1.75736 + 1.75736i 0.116640 + 0.116640i 0.763018 0.646378i \(-0.223717\pi\)
−0.646378 + 0.763018i \(0.723717\pi\)
\(228\) 15.3137 + 10.8284i 1.01418 + 0.717130i
\(229\) 1.65685i 0.109488i −0.998500 0.0547440i \(-0.982566\pi\)
0.998500 0.0547440i \(-0.0174343\pi\)
\(230\) 0 0
\(231\) −0.242641 1.41421i −0.0159646 0.0930484i
\(232\) 15.0711 15.0711i 0.989464 0.989464i
\(233\) 8.34315 8.34315i 0.546578 0.546578i −0.378872 0.925449i \(-0.623688\pi\)
0.925449 + 0.378872i \(0.123688\pi\)
\(234\) 19.3137 6.82843i 1.26258 0.446388i
\(235\) 0 0
\(236\) 15.3137i 0.996838i
\(237\) 5.17157 7.31371i 0.335930 0.475076i
\(238\) −5.65685 5.65685i −0.366679 0.366679i
\(239\) −15.7990 −1.02195 −0.510976 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(240\) 0 0
\(241\) −28.1421 −1.81279 −0.906397 0.422427i \(-0.861178\pi\)
−0.906397 + 0.422427i \(0.861178\pi\)
\(242\) 1.70711 + 1.70711i 0.109737 + 0.109737i
\(243\) −15.5563 + 1.00000i −0.997940 + 0.0641500i
\(244\) 40.1421i 2.56984i
\(245\) 0 0
\(246\) 15.0711 2.58579i 0.960896 0.164864i
\(247\) 5.65685 5.65685i 0.359937 0.359937i
\(248\) −27.5563 + 27.5563i −1.74983 + 1.74983i
\(249\) 12.2426 2.10051i 0.775846 0.133114i
\(250\) 0 0
\(251\) 12.1421i 0.766405i 0.923664 + 0.383202i \(0.125179\pi\)
−0.923664 + 0.383202i \(0.874821\pi\)
\(252\) −4.10051 + 8.58579i −0.258308 + 0.540854i
\(253\) 5.24264 + 5.24264i 0.329602 + 0.329602i
\(254\) −4.82843 −0.302962
\(255\) 0 0
\(256\) −29.9706 −1.87316
\(257\) 3.82843 + 3.82843i 0.238811 + 0.238811i 0.816358 0.577547i \(-0.195990\pi\)
−0.577547 + 0.816358i \(0.695990\pi\)
\(258\) 28.1421 39.7990i 1.75205 2.47778i
\(259\) 6.82843i 0.424298i
\(260\) 0 0
\(261\) 4.82843 + 13.6569i 0.298872 + 0.845338i
\(262\) 2.00000 2.00000i 0.123560 0.123560i
\(263\) −10.2426 + 10.2426i −0.631588 + 0.631588i −0.948466 0.316878i \(-0.897365\pi\)
0.316878 + 0.948466i \(0.397365\pi\)
\(264\) −1.29289 7.53553i −0.0795721 0.463780i
\(265\) 0 0
\(266\) 5.65685i 0.346844i
\(267\) −2.34315 1.65685i −0.143398 0.101398i
\(268\) 13.7279 + 13.7279i 0.838566 + 0.838566i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) −8.48528 −0.515444 −0.257722 0.966219i \(-0.582972\pi\)
−0.257722 + 0.966219i \(0.582972\pi\)
\(272\) −8.48528 8.48528i −0.514496 0.514496i
\(273\) 3.31371 + 2.34315i 0.200555 + 0.141814i
\(274\) 19.8995i 1.20217i
\(275\) 0 0
\(276\) −8.31371 48.4558i −0.500426 2.91670i
\(277\) 1.51472 1.51472i 0.0910106 0.0910106i −0.660136 0.751146i \(-0.729501\pi\)
0.751146 + 0.660136i \(0.229501\pi\)
\(278\) 10.8284 10.8284i 0.649446 0.649446i
\(279\) −8.82843 24.9706i −0.528544 1.49495i
\(280\) 0 0
\(281\) 16.6274i 0.991909i −0.868349 0.495954i \(-0.834818\pi\)
0.868349 0.495954i \(-0.165182\pi\)
\(282\) 4.24264 6.00000i 0.252646 0.357295i
\(283\) 0.928932 + 0.928932i 0.0552193 + 0.0552193i 0.734177 0.678958i \(-0.237568\pi\)
−0.678958 + 0.734177i \(0.737568\pi\)
\(284\) −55.4558 −3.29070
\(285\) 0 0
\(286\) −6.82843 −0.403773
\(287\) 2.14214 + 2.14214i 0.126446 + 0.126446i
\(288\) 2.05025 4.29289i 0.120812 0.252961i
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 1.58579 0.272078i 0.0929604 0.0159495i
\(292\) 0 0
\(293\) 7.65685 7.65685i 0.447318 0.447318i −0.447144 0.894462i \(-0.647559\pi\)
0.894462 + 0.447144i \(0.147559\pi\)
\(294\) 26.0208 4.46447i 1.51756 0.260373i
\(295\) 0 0
\(296\) 36.3848i 2.11482i
\(297\) 5.00000 + 1.41421i 0.290129 + 0.0820610i
\(298\) −17.0711 17.0711i −0.988900 0.988900i
\(299\) −20.9706 −1.21276
\(300\) 0 0
\(301\) 9.65685 0.556612
\(302\) 30.9706 + 30.9706i 1.78216 + 1.78216i
\(303\) 12.8284 18.1421i 0.736974 1.04224i
\(304\) 8.48528i 0.486664i
\(305\) 0 0
\(306\) 27.3137 9.65685i 1.56142 0.552046i
\(307\) −7.89949 + 7.89949i −0.450848 + 0.450848i −0.895636 0.444788i \(-0.853279\pi\)
0.444788 + 0.895636i \(0.353279\pi\)
\(308\) 2.24264 2.24264i 0.127786 0.127786i
\(309\) 1.48528 + 8.65685i 0.0844947 + 0.492471i
\(310\) 0 0
\(311\) 0.142136i 0.00805977i −0.999992 0.00402989i \(-0.998717\pi\)
0.999992 0.00402989i \(-0.00128276\pi\)
\(312\) 17.6569 + 12.4853i 0.999623 + 0.706840i
\(313\) −1.34315 1.34315i −0.0759191 0.0759191i 0.668128 0.744047i \(-0.267096\pi\)
−0.744047 + 0.668128i \(0.767096\pi\)
\(314\) 25.5563 1.44223
\(315\) 0 0
\(316\) 19.7990 1.11378
\(317\) −20.3137 20.3137i −1.14093 1.14093i −0.988280 0.152651i \(-0.951219\pi\)
−0.152651 0.988280i \(-0.548781\pi\)
\(318\) −4.82843 3.41421i −0.270765 0.191460i
\(319\) 4.82843i 0.270340i
\(320\) 0 0
\(321\) −3.41421 19.8995i −0.190563 1.11068i
\(322\) 10.4853 10.4853i 0.584322 0.584322i
\(323\) 8.00000 8.00000i 0.445132 0.445132i
\(324\) −21.6569 26.7990i −1.20316 1.48883i
\(325\) 0 0
\(326\) 21.8995i 1.21290i
\(327\) 8.82843 12.4853i 0.488213 0.690438i
\(328\) 11.4142 + 11.4142i 0.630245 + 0.630245i
\(329\) 1.45584 0.0802633
\(330\) 0 0
\(331\) 10.4853 0.576323 0.288162 0.957582i \(-0.406956\pi\)
0.288162 + 0.957582i \(0.406956\pi\)
\(332\) 19.4142 + 19.4142i 1.06549 + 1.06549i
\(333\) 22.3137 + 10.6569i 1.22278 + 0.583992i
\(334\) 36.6274i 2.00416i
\(335\) 0 0
\(336\) −4.24264 + 0.727922i −0.231455 + 0.0397114i
\(337\) 5.17157 5.17157i 0.281714 0.281714i −0.552079 0.833792i \(-0.686165\pi\)
0.833792 + 0.552079i \(0.186165\pi\)
\(338\) −8.53553 + 8.53553i −0.464272 + 0.464272i
\(339\) −0.414214 + 0.0710678i −0.0224970 + 0.00385987i
\(340\) 0 0
\(341\) 8.82843i 0.478086i
\(342\) −18.4853 8.82843i −0.999570 0.477387i
\(343\) 7.79899 + 7.79899i 0.421106 + 0.421106i
\(344\) 51.4558 2.77431
\(345\) 0 0
\(346\) 28.9706 1.55747
\(347\) −17.8995 17.8995i −0.960895 0.960895i 0.0383684 0.999264i \(-0.487784\pi\)
−0.999264 + 0.0383684i \(0.987784\pi\)
\(348\) −18.4853 + 26.1421i −0.990915 + 1.40137i
\(349\) 30.0000i 1.60586i −0.596071 0.802932i \(-0.703272\pi\)
0.596071 0.802932i \(-0.296728\pi\)
\(350\) 0 0
\(351\) −12.8284 + 7.17157i −0.684731 + 0.382790i
\(352\) −1.12132 + 1.12132i −0.0597666 + 0.0597666i
\(353\) 2.17157 2.17157i 0.115581 0.115581i −0.646951 0.762532i \(-0.723956\pi\)
0.762532 + 0.646951i \(0.223956\pi\)
\(354\) −2.82843 16.4853i −0.150329 0.876183i
\(355\) 0 0
\(356\) 6.34315i 0.336186i
\(357\) 4.68629 + 3.31371i 0.248025 + 0.175380i
\(358\) −7.07107 7.07107i −0.373718 0.373718i
\(359\) −6.14214 −0.324170 −0.162085 0.986777i \(-0.551822\pi\)
−0.162085 + 0.986777i \(0.551822\pi\)
\(360\) 0 0
\(361\) 11.0000 0.578947
\(362\) 9.65685 + 9.65685i 0.507553 + 0.507553i
\(363\) −1.41421 1.00000i −0.0742270 0.0524864i
\(364\) 8.97056i 0.470185i
\(365\) 0 0
\(366\) −7.41421 43.2132i −0.387547 2.25879i
\(367\) 20.8995 20.8995i 1.09094 1.09094i 0.0955170 0.995428i \(-0.469550\pi\)
0.995428 0.0955170i \(-0.0304504\pi\)
\(368\) 15.7279 15.7279i 0.819875 0.819875i
\(369\) −10.3431 + 3.65685i −0.538443 + 0.190368i
\(370\) 0 0
\(371\) 1.17157i 0.0608250i
\(372\) 33.7990 47.7990i 1.75240 2.47826i
\(373\) −20.4853 20.4853i −1.06069 1.06069i −0.998035 0.0626522i \(-0.980044\pi\)
−0.0626522 0.998035i \(-0.519956\pi\)
\(374\) −9.65685 −0.499344
\(375\) 0 0
\(376\) 7.75736 0.400055
\(377\) 9.65685 + 9.65685i 0.497353 + 0.497353i
\(378\) 2.82843 10.0000i 0.145479 0.514344i
\(379\) 0.142136i 0.00730102i −0.999993 0.00365051i \(-0.998838\pi\)
0.999993 0.00365051i \(-0.00116200\pi\)
\(380\) 0 0
\(381\) 3.41421 0.585786i 0.174915 0.0300107i
\(382\) −19.3137 + 19.3137i −0.988175 + 0.988175i
\(383\) 8.07107 8.07107i 0.412412 0.412412i −0.470166 0.882578i \(-0.655806\pi\)
0.882578 + 0.470166i \(0.155806\pi\)
\(384\) 35.0919 6.02082i 1.79078 0.307248i
\(385\) 0 0
\(386\) 27.3137i 1.39023i
\(387\) −15.0711 + 31.5563i −0.766105 + 1.60410i
\(388\) 2.51472 + 2.51472i 0.127665 + 0.127665i
\(389\) −5.31371 −0.269416 −0.134708 0.990885i \(-0.543010\pi\)
−0.134708 + 0.990885i \(0.543010\pi\)
\(390\) 0 0
\(391\) −29.6569 −1.49981
\(392\) 19.7071 + 19.7071i 0.995359 + 0.995359i
\(393\) −1.17157 + 1.65685i −0.0590980 + 0.0835772i
\(394\) 48.2843i 2.43253i
\(395\) 0 0
\(396\) 3.82843 + 10.8284i 0.192386 + 0.544149i
\(397\) −11.8284 + 11.8284i −0.593652 + 0.593652i −0.938616 0.344964i \(-0.887891\pi\)
0.344964 + 0.938616i \(0.387891\pi\)
\(398\) −4.24264 + 4.24264i −0.212664 + 0.212664i
\(399\) −0.686292 4.00000i −0.0343575 0.200250i
\(400\) 0 0
\(401\) 24.3431i 1.21564i 0.794075 + 0.607819i \(0.207956\pi\)
−0.794075 + 0.607819i \(0.792044\pi\)
\(402\) −17.3137 12.2426i −0.863529 0.610607i
\(403\) −17.6569 17.6569i −0.879551 0.879551i
\(404\) 49.1127 2.44345
\(405\) 0 0
\(406\) −9.65685 −0.479262
\(407\) −5.82843 5.82843i −0.288904 0.288904i
\(408\) 24.9706 + 17.6569i 1.23623 + 0.874145i
\(409\) 1.51472i 0.0748980i −0.999299 0.0374490i \(-0.988077\pi\)
0.999299 0.0374490i \(-0.0119232\pi\)
\(410\) 0 0
\(411\) 2.41421 + 14.0711i 0.119084 + 0.694075i
\(412\) −13.7279 + 13.7279i −0.676326 + 0.676326i
\(413\) 2.34315 2.34315i 0.115299 0.115299i
\(414\) 17.8995 + 50.6274i 0.879712 + 2.48820i
\(415\) 0 0
\(416\) 4.48528i 0.219909i
\(417\) −6.34315 + 8.97056i −0.310625 + 0.439290i
\(418\) 4.82843 + 4.82843i 0.236166 + 0.236166i
\(419\) 35.4558 1.73213 0.866066 0.499930i \(-0.166641\pi\)
0.866066 + 0.499930i \(0.166641\pi\)
\(420\) 0 0
\(421\) −4.00000 −0.194948 −0.0974740 0.995238i \(-0.531076\pi\)
−0.0974740 + 0.995238i \(0.531076\pi\)
\(422\) −21.3137 21.3137i −1.03754 1.03754i
\(423\) −2.27208 + 4.75736i −0.110472 + 0.231311i
\(424\) 6.24264i 0.303169i
\(425\) 0 0
\(426\) 59.6985 10.2426i 2.89240 0.496258i
\(427\) 6.14214 6.14214i 0.297239 0.297239i
\(428\) 31.5563 31.5563i 1.52533 1.52533i
\(429\) 4.82843 0.828427i 0.233119 0.0399968i
\(430\) 0 0
\(431\) 17.6569i 0.850501i −0.905076 0.425250i \(-0.860186\pi\)
0.905076 0.425250i \(-0.139814\pi\)
\(432\) 4.24264 15.0000i 0.204124 0.721688i
\(433\) −22.3137 22.3137i −1.07233 1.07233i −0.997172 0.0751567i \(-0.976054\pi\)
−0.0751567 0.997172i \(-0.523946\pi\)
\(434\) 17.6569 0.847556
\(435\) 0 0
\(436\) 33.7990 1.61868
\(437\) 14.8284 + 14.8284i 0.709340 + 0.709340i
\(438\) 0 0
\(439\) 15.3137i 0.730883i 0.930834 + 0.365442i \(0.119082\pi\)
−0.930834 + 0.365442i \(0.880918\pi\)
\(440\) 0 0
\(441\) −17.8579 + 6.31371i −0.850374 + 0.300653i
\(442\) 19.3137 19.3137i 0.918659 0.918659i
\(443\) −29.2426 + 29.2426i −1.38936 + 1.38936i −0.562696 + 0.826664i \(0.690236\pi\)
−0.826664 + 0.562696i \(0.809764\pi\)
\(444\) 9.24264 + 53.8701i 0.438636 + 2.55656i
\(445\) 0 0
\(446\) 49.6985i 2.35329i
\(447\) 14.1421 + 10.0000i 0.668900 + 0.472984i
\(448\) 5.75736 + 5.75736i 0.272010 + 0.272010i
\(449\) 36.9706 1.74475 0.872374 0.488838i \(-0.162579\pi\)
0.872374 + 0.488838i \(0.162579\pi\)
\(450\) 0 0
\(451\) 3.65685 0.172195
\(452\) −0.656854 0.656854i −0.0308958 0.0308958i
\(453\) −25.6569 18.1421i −1.20546 0.852392i
\(454\) 6.00000i 0.281594i
\(455\) 0 0
\(456\) −3.65685 21.3137i −0.171248 0.998106i
\(457\) −10.4853 + 10.4853i −0.490481 + 0.490481i −0.908458 0.417977i \(-0.862739\pi\)
0.417977 + 0.908458i \(0.362739\pi\)
\(458\) −2.82843 + 2.82843i −0.132164 + 0.132164i
\(459\) −18.1421 + 10.1421i −0.846802 + 0.473394i
\(460\) 0 0
\(461\) 30.4853i 1.41984i −0.704282 0.709921i \(-0.748731\pi\)
0.704282 0.709921i \(-0.251269\pi\)
\(462\) −2.00000 + 2.82843i −0.0930484 + 0.131590i
\(463\) 13.7279 + 13.7279i 0.637991 + 0.637991i 0.950059 0.312069i \(-0.101022\pi\)
−0.312069 + 0.950059i \(0.601022\pi\)
\(464\) −14.4853 −0.672462
\(465\) 0 0
\(466\) −28.4853 −1.31956
\(467\) 2.41421 + 2.41421i 0.111716 + 0.111716i 0.760755 0.649039i \(-0.224829\pi\)
−0.649039 + 0.760755i \(0.724829\pi\)
\(468\) −29.3137 14.0000i −1.35503 0.647150i
\(469\) 4.20101i 0.193985i
\(470\) 0 0
\(471\) −18.0711 + 3.10051i −0.832671 + 0.142864i
\(472\) 12.4853 12.4853i 0.574682 0.574682i
\(473\) 8.24264 8.24264i 0.378997 0.378997i
\(474\) −21.3137 + 3.65685i −0.978971 + 0.167965i
\(475\) 0 0
\(476\) 12.6863i 0.581475i
\(477\) 3.82843 + 1.82843i 0.175292 + 0.0837179i
\(478\) 26.9706 + 26.9706i 1.23360 + 1.23360i
\(479\) 1.85786 0.0848880 0.0424440 0.999099i \(-0.486486\pi\)
0.0424440 + 0.999099i \(0.486486\pi\)
\(480\) 0 0
\(481\) 23.3137 1.06301
\(482\) 48.0416 + 48.0416i 2.18824 + 2.18824i
\(483\) −6.14214 + 8.68629i −0.279477 + 0.395240i
\(484\) 3.82843i 0.174019i
\(485\) 0 0
\(486\) 28.2635 + 24.8492i 1.28206 + 1.12718i
\(487\) 13.7279 13.7279i 0.622072 0.622072i −0.323989 0.946061i \(-0.605024\pi\)
0.946061 + 0.323989i \(0.105024\pi\)
\(488\) 32.7279 32.7279i 1.48152 1.48152i
\(489\) −2.65685 15.4853i −0.120147 0.700269i
\(490\) 0 0
\(491\) 20.0000i 0.902587i −0.892375 0.451294i \(-0.850963\pi\)
0.892375 0.451294i \(-0.149037\pi\)
\(492\) −19.7990 14.0000i −0.892607 0.631169i
\(493\) 13.6569 + 13.6569i 0.615074 + 0.615074i
\(494\) −19.3137 −0.868965
\(495\) 0 0
\(496\) 26.4853 1.18922
\(497\) 8.48528 + 8.48528i 0.380617 + 0.380617i
\(498\) −24.4853 17.3137i −1.09721 0.775846i
\(499\) 19.1716i 0.858237i 0.903248 + 0.429119i \(0.141176\pi\)
−0.903248 + 0.429119i \(0.858824\pi\)
\(500\) 0 0
\(501\) −4.44365 25.8995i −0.198528 1.15710i
\(502\) 20.7279 20.7279i 0.925132 0.925132i
\(503\) 15.0711 15.0711i 0.671986 0.671986i −0.286188 0.958174i \(-0.592388\pi\)
0.958174 + 0.286188i \(0.0923881\pi\)
\(504\) 10.3431 3.65685i 0.460720 0.162889i
\(505\) 0 0
\(506\) 17.8995i 0.795730i
\(507\) 5.00000 7.07107i 0.222058 0.314037i
\(508\) 5.41421 + 5.41421i 0.240217 + 0.240217i
\(509\) −24.3431 −1.07899 −0.539495 0.841988i \(-0.681385\pi\)
−0.539495 + 0.841988i \(0.681385\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.0919 + 22.0919i 0.976333 + 0.976333i
\(513\) 14.1421 + 4.00000i 0.624391 + 0.176604i
\(514\) 13.0711i 0.576540i
\(515\) 0 0
\(516\) −76.1838 + 13.0711i −3.35380 + 0.575422i
\(517\) 1.24264 1.24264i 0.0546513 0.0546513i
\(518\) −11.6569 + 11.6569i −0.512173 + 0.512173i
\(519\) −20.4853 + 3.51472i −0.899204 + 0.154279i
\(520\) 0 0
\(521\) 16.3431i 0.716006i −0.933720 0.358003i \(-0.883458\pi\)
0.933720 0.358003i \(-0.116542\pi\)
\(522\) 15.0711 31.5563i 0.659643 1.38118i
\(523\) −15.2132 15.2132i −0.665227 0.665227i 0.291380 0.956607i \(-0.405885\pi\)
−0.956607 + 0.291380i \(0.905885\pi\)
\(524\) −4.48528 −0.195940
\(525\) 0 0
\(526\) 34.9706 1.52479
\(527\) −24.9706 24.9706i −1.08773 1.08773i
\(528\) −3.00000 + 4.24264i −0.130558 + 0.184637i
\(529\) 31.9706i 1.39002i
\(530\) 0 0
\(531\) 4.00000 + 11.3137i 0.173585 + 0.490973i
\(532\) 6.34315 6.34315i 0.275010 0.275010i
\(533\) −7.31371 + 7.31371i −0.316792 + 0.316792i
\(534\) 1.17157 + 6.82843i 0.0506989 + 0.295495i
\(535\) 0 0
\(536\) 22.3848i 0.966875i
\(537\) 5.85786 + 4.14214i 0.252786 + 0.178746i
\(538\) −23.8995 23.8995i −1.03038 1.03038i
\(539\) 6.31371 0.271951
\(540\) 0 0
\(541\) −33.3137 −1.43227 −0.716134 0.697963i \(-0.754090\pi\)
−0.716134 + 0.697963i \(0.754090\pi\)
\(542\) 14.4853 + 14.4853i 0.622196 + 0.622196i
\(543\) −8.00000 5.65685i −0.343313 0.242759i
\(544\) 6.34315i 0.271960i
\(545\) 0 0
\(546\) −1.65685 9.65685i −0.0709068 0.413275i
\(547\) −21.8995 + 21.8995i −0.936355 + 0.936355i −0.998092 0.0617376i \(-0.980336\pi\)
0.0617376 + 0.998092i \(0.480336\pi\)
\(548\) −22.3137 + 22.3137i −0.953194 + 0.953194i
\(549\) 10.4853 + 29.6569i 0.447501 + 1.26572i
\(550\) 0 0
\(551\) 13.6569i 0.581802i
\(552\) −32.7279 + 46.2843i −1.39299 + 1.96999i
\(553\) −3.02944 3.02944i −0.128825 0.128825i
\(554\) −5.17157 −0.219719
\(555\) 0 0
\(556\) −24.2843 −1.02988
\(557\) −24.9706 24.9706i −1.05804 1.05804i −0.998209 0.0598280i \(-0.980945\pi\)
−0.0598280 0.998209i \(-0.519055\pi\)
\(558\) −27.5563 + 57.6985i −1.16655 + 2.44257i
\(559\) 32.9706i 1.39451i
\(560\) 0 0
\(561\) 6.82843 1.17157i 0.288296 0.0494638i
\(562\) −28.3848 + 28.3848i −1.19734 + 1.19734i
\(563\) 9.89949 9.89949i 0.417214 0.417214i −0.467028 0.884242i \(-0.654675\pi\)
0.884242 + 0.467028i \(0.154675\pi\)
\(564\) −11.4853 + 1.97056i −0.483618 + 0.0829757i
\(565\) 0 0
\(566\) 3.17157i 0.133311i
\(567\) −0.786797 + 7.41421i −0.0330423 + 0.311368i
\(568\) 45.2132 + 45.2132i 1.89710 + 1.89710i
\(569\) 39.6569 1.66250 0.831251 0.555897i \(-0.187625\pi\)
0.831251 + 0.555897i \(0.187625\pi\)
\(570\) 0 0
\(571\) 18.3431 0.767637 0.383818 0.923409i \(-0.374609\pi\)
0.383818 + 0.923409i \(0.374609\pi\)
\(572\) 7.65685 + 7.65685i 0.320149 + 0.320149i
\(573\) 11.3137 16.0000i 0.472637 0.668410i
\(574\) 7.31371i 0.305268i
\(575\) 0 0
\(576\) −27.7990 + 9.82843i −1.15829 + 0.409518i
\(577\) −17.0000 + 17.0000i −0.707719 + 0.707719i −0.966055 0.258336i \(-0.916826\pi\)
0.258336 + 0.966055i \(0.416826\pi\)
\(578\) −1.70711 + 1.70711i −0.0710063 + 0.0710063i
\(579\) −3.31371 19.3137i −0.137713 0.802650i
\(580\) 0 0
\(581\) 5.94113i 0.246479i
\(582\) −3.17157 2.24264i −0.131466 0.0929604i
\(583\) −1.00000 1.00000i −0.0414158 0.0414158i
\(584\) 0 0
\(585\) 0 0
\(586\) −26.1421 −1.07992
\(587\) 2.41421 + 2.41421i 0.0996453 + 0.0996453i 0.755172 0.655527i \(-0.227553\pi\)
−0.655527 + 0.755172i \(0.727553\pi\)
\(588\) −34.1838 24.1716i −1.40971 0.996819i
\(589\) 24.9706i 1.02889i
\(590\) 0 0
\(591\) 5.85786 + 34.1421i 0.240960 + 1.40442i
\(592\) −17.4853 + 17.4853i −0.718641 + 0.718641i
\(593\) 34.1421 34.1421i 1.40205 1.40205i 0.608481 0.793568i \(-0.291779\pi\)
0.793568 0.608481i \(-0.208221\pi\)
\(594\) −6.12132 10.9497i −0.251161 0.449274i
\(595\) 0 0
\(596\) 38.2843i 1.56818i
\(597\) 2.48528 3.51472i 0.101716 0.143848i
\(598\) 35.7990 + 35.7990i 1.46393 + 1.46393i
\(599\) −47.4558 −1.93899 −0.969497 0.245105i \(-0.921178\pi\)
−0.969497 + 0.245105i \(0.921178\pi\)
\(600\) 0 0
\(601\) 23.4558 0.956784 0.478392 0.878146i \(-0.341220\pi\)
0.478392 + 0.878146i \(0.341220\pi\)
\(602\) −16.4853 16.4853i −0.671890 0.671890i
\(603\) 13.7279 + 6.55635i 0.559044 + 0.266995i
\(604\) 69.4558i 2.82612i
\(605\) 0 0
\(606\) −52.8701 + 9.07107i −2.14770 + 0.368487i
\(607\) 2.10051 2.10051i 0.0852569 0.0852569i −0.663192 0.748449i \(-0.730799\pi\)
0.748449 + 0.663192i \(0.230799\pi\)
\(608\) −3.17157 + 3.17157i −0.128624 + 0.128624i
\(609\) 6.82843 1.17157i 0.276702 0.0474745i
\(610\) 0 0
\(611\) 4.97056i 0.201087i
\(612\) −41.4558 19.7990i −1.67575 0.800327i
\(613\) 16.0000 + 16.0000i 0.646234 + 0.646234i 0.952081 0.305847i \(-0.0989395\pi\)
−0.305847 + 0.952081i \(0.598940\pi\)
\(614\) 26.9706 1.08844
\(615\) 0 0
\(616\) −3.65685 −0.147339
\(617\) 24.1716 + 24.1716i 0.973111 + 0.973111i 0.999648 0.0265370i \(-0.00844797\pi\)
−0.0265370 + 0.999648i \(0.508448\pi\)
\(618\) 12.2426 17.3137i 0.492471 0.696459i
\(619\) 23.3137i 0.937057i −0.883448 0.468529i \(-0.844784\pi\)
0.883448 0.468529i \(-0.155216\pi\)
\(620\) 0 0
\(621\) −18.7990 33.6274i −0.754377 1.34942i
\(622\) −0.242641 + 0.242641i −0.00972901 + 0.00972901i
\(623\) −0.970563 + 0.970563i −0.0388848 + 0.0388848i
\(624\) −2.48528 14.4853i −0.0994909 0.579875i
\(625\) 0 0
\(626\) 4.58579i 0.183285i
\(627\) −4.00000 2.82843i −0.159745 0.112956i
\(628\) −28.6569 28.6569i −1.14353 1.14353i
\(629\) 32.9706 1.31462
\(630\) 0 0
\(631\) 16.9706 0.675587 0.337794 0.941220i \(-0.390319\pi\)
0.337794 + 0.941220i \(0.390319\pi\)
\(632\) −16.1421 16.1421i −0.642100 0.642100i
\(633\) 17.6569 + 12.4853i 0.701797 + 0.496245i
\(634\) 69.3553i 2.75445i
\(635\) 0 0
\(636\) 1.58579 + 9.24264i 0.0628805 + 0.366495i
\(637\) −12.6274 + 12.6274i −0.500316 + 0.500316i
\(638\) −8.24264 + 8.24264i −0.326329 + 0.326329i
\(639\) −40.9706 + 14.4853i −1.62077 + 0.573029i
\(640\) 0 0
\(641\) 12.6274i 0.498753i 0.968407 + 0.249376i \(0.0802257\pi\)
−0.968407 + 0.249376i \(0.919774\pi\)
\(642\) −28.1421 + 39.7990i −1.11068 + 1.57074i
\(643\) 0.757359 + 0.757359i 0.0298673 + 0.0298673i 0.721883 0.692015i \(-0.243277\pi\)
−0.692015 + 0.721883i \(0.743277\pi\)
\(644\) −23.5147 −0.926610
\(645\) 0 0
\(646\) −27.3137 −1.07464
\(647\) −13.7279 13.7279i −0.539700 0.539700i 0.383741 0.923441i \(-0.374636\pi\)
−0.923441 + 0.383741i \(0.874636\pi\)
\(648\) −4.19239 + 39.5061i −0.164693 + 1.55195i
\(649\) 4.00000i 0.157014i
\(650\) 0 0
\(651\) −12.4853 + 2.14214i −0.489337 + 0.0839569i
\(652\) 24.5563 24.5563i 0.961701 0.961701i
\(653\) −2.65685 + 2.65685i −0.103971 + 0.103971i −0.757179 0.653208i \(-0.773423\pi\)
0.653208 + 0.757179i \(0.273423\pi\)
\(654\) −36.3848 + 6.24264i −1.42276 + 0.244107i
\(655\) 0 0
\(656\) 10.9706i 0.428329i
\(657\) 0 0
\(658\) −2.48528 2.48528i −0.0968864 0.0968864i
\(659\) −8.97056 −0.349444 −0.174722 0.984618i \(-0.555903\pi\)
−0.174722 + 0.984618i \(0.555903\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −17.8995 17.8995i −0.695684 0.695684i
\(663\) −11.3137 + 16.0000i −0.439388 + 0.621389i
\(664\) 31.6569i 1.22852i
\(665\) 0 0
\(666\) −19.8995 56.2843i −0.771090 2.18097i
\(667\) −25.3137 + 25.3137i −0.980151 + 0.980151i
\(668\) 41.0711 41.0711i 1.58909 1.58909i
\(669\) −6.02944 35.1421i −0.233112 1.35867i
\(670\) 0 0
\(671\) 10.4853i 0.404780i
\(672\) −1.85786 1.31371i −0.0716687 0.0506774i
\(673\) 33.6569 + 33.6569i 1.29738 + 1.29738i 0.930120 + 0.367257i \(0.119703\pi\)
0.367257 + 0.930120i \(0.380297\pi\)
\(674\) −17.6569 −0.680117
\(675\) 0 0
\(676\) 19.1421 0.736236
\(677\) 8.34315 + 8.34315i 0.320653 + 0.320653i 0.849018 0.528365i \(-0.177195\pi\)
−0.528365 + 0.849018i \(0.677195\pi\)
\(678\) 0.828427 + 0.585786i 0.0318156 + 0.0224970i
\(679\) 0.769553i 0.0295327i
\(680\) 0 0
\(681\) 0.727922 + 4.24264i 0.0278940 + 0.162578i
\(682\) 15.0711 15.0711i 0.577101 0.577101i
\(683\) −17.7279 + 17.7279i −0.678340 + 0.678340i −0.959624 0.281284i \(-0.909240\pi\)
0.281284 + 0.959624i \(0.409240\pi\)
\(684\) 10.8284 + 30.6274i 0.414035 + 1.17107i
\(685\) 0 0
\(686\) 26.6274i 1.01664i
\(687\) 1.65685 2.34315i 0.0632129 0.0893966i
\(688\) −24.7279 24.7279i −0.942743 0.942743i
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −32.4853 32.4853i −1.23491 1.23491i
\(693\) 1.07107 2.24264i 0.0406865 0.0851909i
\(694\) 61.1127i 2.31981i
\(695\) 0 0
\(696\) 36.3848 6.24264i 1.37916 0.236627i
\(697\) −10.3431 + 10.3431i −0.391775 + 0.391775i
\(698\) −51.2132 + 51.2132i −1.93845 + 1.93845i
\(699\) 20.1421 3.45584i 0.761846 0.130712i
\(700\) 0 0
\(701\) 21.3137i 0.805008i −0.915418 0.402504i \(-0.868140\pi\)
0.915418 0.402504i \(-0.131860\pi\)
\(702\) 34.1421 + 9.65685i 1.28861 + 0.364474i
\(703\) −16.4853 16.4853i −0.621754 0.621754i
\(704\) 9.82843 0.370423
\(705\) 0 0
\(706\) −7.41421 −0.279038
\(707\) −7.51472 7.51472i −0.282620 0.282620i
\(708\) −15.3137 + 21.6569i −0.575524 + 0.813914i
\(709\) 6.68629i 0.251109i 0.992087 + 0.125554i \(0.0400710\pi\)
−0.992087 + 0.125554i \(0.959929\pi\)
\(710\) 0 0
\(711\) 14.6274 5.17157i 0.548571 0.193949i
\(712\) −5.17157 + 5.17157i −0.193813 + 0.193813i
\(713\) 46.2843 46.2843i 1.73336 1.73336i
\(714\) −2.34315 13.6569i −0.0876900 0.511095i
\(715\) 0 0
\(716\) 15.8579i 0.592636i
\(717\) −22.3431 15.7990i −0.834420 0.590024i
\(718\) 10.4853 + 10.4853i 0.391307 + 0.391307i
\(719\) −50.7696 −1.89338 −0.946692 0.322139i \(-0.895598\pi\)
−0.946692 + 0.322139i \(0.895598\pi\)
\(720\) 0 0
\(721\) 4.20101 0.156454
\(722\) −18.7782 18.7782i −0.698851 0.698851i
\(723\) −39.7990 28.1421i −1.48014 1.04662i
\(724\) 21.6569i 0.804871i
\(725\) 0 0
\(726\) 0.707107 + 4.12132i 0.0262432 + 0.152957i
\(727\) 22.2132 22.2132i 0.823842 0.823842i −0.162815 0.986657i \(-0.552057\pi\)
0.986657 + 0.162815i \(0.0520572\pi\)
\(728\) 7.31371 7.31371i 0.271064 0.271064i
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 46.6274i 1.72458i
\(732\) −40.1421 + 56.7696i −1.48370 + 2.09826i
\(733\) 35.7990 + 35.7990i 1.32227 + 1.32227i 0.911938 + 0.410328i \(0.134586\pi\)
0.410328 + 0.911938i \(0.365414\pi\)
\(734\) −71.3553 −2.63377
\(735\) 0 0
\(736\) 11.7574 0.433382
\(737\) −3.58579 3.58579i −0.132084 0.132084i
\(738\) 23.8995 + 11.4142i 0.879753 + 0.420163i
\(739\) 30.6274i 1.12665i 0.826236 + 0.563324i \(0.190478\pi\)
−0.826236 + 0.563324i \(0.809522\pi\)
\(740\) 0 0
\(741\) 13.6569 2.34315i 0.501697 0.0860776i
\(742\) −2.00000 + 2.00000i −0.0734223 + 0.0734223i
\(743\) 22.0416 22.0416i 0.808629 0.808629i −0.175797 0.984426i \(-0.556250\pi\)
0.984426 + 0.175797i \(0.0562504\pi\)
\(744\) −66.5269 + 11.4142i −2.43899 + 0.418465i
\(745\) 0 0
\(746\) 69.9411i 2.56073i
\(747\) 19.4142 + 9.27208i 0.710329 + 0.339248i
\(748\) 10.8284 + 10.8284i 0.395927 + 0.395927i
\(749\) −9.65685 −0.352854
\(750\) 0 0
\(751\) −1.37258 −0.0500863 −0.0250431 0.999686i \(-0.507972\pi\)
−0.0250431 + 0.999686i \(0.507972\pi\)
\(752\) −3.72792 3.72792i −0.135943 0.135943i
\(753\) −12.1421 + 17.1716i −0.442484 + 0.625767i
\(754\) 32.9706i 1.20072i
\(755\) 0 0
\(756\) −14.3848 + 8.04163i −0.523169 + 0.292471i
\(757\) −5.82843 + 5.82843i −0.211838 + 0.211838i −0.805048 0.593210i \(-0.797860\pi\)
0.593210 + 0.805048i \(0.297860\pi\)
\(758\) −0.242641 + 0.242641i −0.00881311 + 0.00881311i
\(759\) 2.17157 + 12.6569i 0.0788231 + 0.459415i
\(760\) 0 0
\(761\) 18.4853i 0.670091i 0.942202 + 0.335045i \(0.108752\pi\)
−0.942202 + 0.335045i \(0.891248\pi\)
\(762\) −6.82843 4.82843i −0.247368 0.174915i
\(763\) −5.17157 5.17157i −0.187224 0.187224i
\(764\) 43.3137 1.56703
\(765\) 0 0
\(766\) −27.5563 −0.995651
\(767\) 8.00000 + 8.00000i 0.288863 + 0.288863i
\(768\) −42.3848 29.9706i −1.52943 1.08147i
\(769\) 7.37258i 0.265862i 0.991125 + 0.132931i \(0.0424389\pi\)
−0.991125 + 0.132931i \(0.957561\pi\)
\(770\) 0 0
\(771\) 1.58579 + 9.24264i 0.0571107 + 0.332866i
\(772\) 30.6274 30.6274i 1.10230 1.10230i
\(773\) −0.656854 + 0.656854i −0.0236254 + 0.0236254i −0.718821 0.695195i \(-0.755318\pi\)
0.695195 + 0.718821i \(0.255318\pi\)
\(774\) 79.5980 28.1421i 2.86109 1.01155i
\(775\) 0 0
\(776\) 4.10051i 0.147200i
\(777\) 6.82843 9.65685i 0.244968 0.346438i
\(778\) 9.07107 + 9.07107i 0.325214 + 0.325214i
\(779\) 10.3431 0.370582
\(780\) 0 0
\(781\) 14.4853 0.518324
\(782\) 50.6274 + 50.6274i 1.81043 + 1.81043i
\(783\) −6.82843 + 24.1421i −0.244028 + 0.862770i
\(784\) 18.9411i